Annealed and quenched limit theorems for random expanding dynamical systems

Abstract

In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a central limit theorem, a large deviation principle, a local limit theorem, and an almost sure invariance principle. We also discuss the quenched central limit theorem, dynamical Borel-Cantelli lemmas, Erdös-Rényi laws and concentration inequalities.

Appeared online in Probability Theory and Related Fields

References in corpus (5)

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Cited by in corpus (19)

• A spectral approach for quenched limit theorems for random expanding dynamical systems
• Almost sure invariance principle for random piecewise expanding maps
• Central limit theorems for sequential and random intermittent dynamical systems
• Limit theorems for some time dependent expanding dynamical systems
• Limit theorems for some skew products with mixing base maps
• Limit theorems for random expanding or hyperbolic dynamical systems and vector-valued observables
• Loss of memory and moment bounds for nonstationary intermittent dynamical systems
• Local limit theorem for randomly deforming billiards
• Quenched normal approximation for random sequences of transformations
• Countable Alphabet Random Subhifts of finite type with weakly positive transfer operator
• Central limit theorems with a rate of convergence for time-dependent intermittent maps
• Stability and limit theorems for sequences of uniformly hyperbolic dynamics
• An Almost Sure Invariance Principle for Several Classes of Random Dynamical Systems
• Suppression of Quasiperiodicity in Circle Maps with Quenched Disorder
• Distribution of cycles for one-dimensional random dynamical systems
• Stable laws for random dynamical systems
• Complex projective metrics on Young towers, countable sub-shifts and other countable covering maps
• The random continued fraction transformation
• Concentration inequalities for sequential dynamical systems of the unit interval